Recovering Subjective Probability Distributions

Abstract

This study proposes a direct estimation method for recovering subjective probability distributions from option prices. We find that the subjective cumulative distribution function and subjective statistics are represented as static portfolios composed of plain vanilla options. The portfolio weights of the options are determined by the levels of the reciprocal of the pricing kernel and their differentiations. Using options data, we investigate the historical behavior of subjective probability distributions of returns on the S&P 500 index. We also analyze subjective equity risk premiums and subjective variance risk premiums, which can be regarded as ex-ante risk premiums.

Keywords: subjective probability distribution; reciprocal kernel; risk aversion; static option portfolio; subjective risk premium

JEL Classification: G12, G17